Refined theories may be needed for vibration analysis of structures with overhang

The effect of shear deformation and rotary inertia terms on the free vibrat ion of a beam with overhang was investigated. A recently proposed modified Timoshenko-type equations of motion were used to analyze the vibration of t he structure. Two different sets of boundary conditions, with either a fixe d or hinged end support, were studied. The results were compared with those obtained for the classical Bernoulli-Euler beam theory. The comparison sho ws that for a hinged end beam with very long overhang, where the span betwe en the supports is less than one tenth of the overall beam length, the clas sical theory significantly overestimates the values of the fundamental natu ral frequencies, even for isotropic shear rigidity. On the other hand, the span effect is reversed for the clamped end beam, for which a relatively si gnificant difference between the classical theory and shear theory results may occur only for a long span. For transversely isotropic beams, the refin ed theory predictions of the fundamental natural frequencies may be much sm aller than those obtained through the rigid shear theory, especially for sh ort span hinged end beams and long span clamped end beams. (C) 1999 Elsevie r Science Ltd. All rights reserved.